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Decision-Making for the Lifetime Performance Index.

Basim S O Alsaedi1, M M Abd El-Raouf2, E H Hafez3

  • 1Department of Statistics, Faculty of Science, University of Tabuk, Tabuk, Saudi Arabia.

Computational Intelligence and Neuroscience
|August 2, 2021
PubMed
Summary

This study develops a maximum likelihood estimator (MLE) for the lifetime performance index (Cpk) using the mixture Rayleigh-Half Normal distribution. This method aids in assessing product lifespan efficiency and supplier selection with censored data.

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Area of Science:

  • Statistics
  • Reliability Engineering
  • Quality Control

Background:

  • The lifetime performance index (Cpk) is crucial for evaluating product quality and reliability.
  • Assessing Cpk with progressively type-II right-censored data presents statistical challenges.
  • The mixture Rayleigh-Half Normal (RHN) distribution offers a flexible model for certain lifetime data.

Purpose of the Study:

  • To develop a Maximum Likelihood Estimator (MLE) for the lifetime performance index (Cpk) of the mixture Rayleigh-Half Normal (RHN) distribution.
  • To establish an asymptotic normal distribution for the MLE of Cpk to facilitate performance evaluation.
  • To provide a hypothesis testing framework for assessing product lifetime efficiency and aiding supplier selection.

Main Methods:

  • Derivation of the Maximum Likelihood Estimator (MLE) for Cpk under the RHN distribution.
  • Utilizing progressively type-II right-censored samples.
  • Constructing an asymptotic normal distribution for the MLE.
  • Developing hypothesis testing procedures.

Main Results:

  • An MLE for Cpk was successfully developed for the RHN distribution under censoring.
  • The asymptotic normality of the MLE was established, enabling confidence interval construction and hypothesis testing.
  • The proposed methodology was illustrated with two real-world data examples.

Conclusions:

  • The developed MLE provides a robust method for estimating product lifetime performance index (Cpk) with censored RHN data.
  • The hypothesis testing framework effectively assesses product reliability and can be used as a supplier selection tool.
  • The practical application of the method is demonstrated through real data analysis.